A quantity Q is formulated as X^-2 Y^3/2 Z... | Measurements & Errors

JEE MAIN 2025

08-004-2025 S2

Question

A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional errors of $0.1,0.2$ and 0.5 , respectively in measurement. The maximum fractional error of Q is

Select the correct option:

0.6

0.7

0.1

0.8

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Solution

$\begin{aligned} & \text { Fractional error }=2 \frac{\Delta X}{X}+\frac{3}{2} \frac{\Delta Y}{Y}+\frac{2}{5} \frac{\Delta Z}{Z} \\ & =2(0.1)+\frac{3}{2}(0.2)+\frac{2}{5}(0.5) \\ & =0.2+0.3+0.2=0.7\end{aligned}$

Question Tags

JEE Main

Physics

Easy

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